Bilinear boundary optimal control of a Kirchhoff plate equation

Abstract

This work shows that a problem of boundary optimal control of a Kirchhoff plate equation has a solution that we characterized using the differentiability of a functional cost. The Kirchhoff plate equation is governed by bilinear control acting on the boundary, in which non-linear terms are constructed by multiplication of the control vector and the state one. The question is to obtain a distributed control which minimizes a function cost constituted of the deviation between a desired state and the reached one, and the energy term. The purpose of this study is to prove that an optimal control exists, and it is characterized as a solution to an optimality system. Thus, We show that the problem of bilinear boundary control has a unique solution if the final time is sufficiently small.

Keywords

• Kirchhoff plate equation
• Boundary bilinear control
• Optimal control problem